A196946 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,1,0,2,3 for x=0,1,2,3,4

6, 136, 1416, 18060, 220433, 2711711, 33344883, 410312728, 5047886243, 62090427845, 763762342576, 9395250084215, 115573099523164, 1421680898385700, 17488281737625729, 215125917361968970, 2646296681161997258

Offset

1,1

Comments

Every 0 is next to 0 4's, every 1 is next to 1 1's, every 2 is next to 2 0's, every 3 is next to 3 2's, every 4 is next to 4 3's

Column 4 of A196950

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 3*a(n-1) +49*a(n-2) +466*a(n-3) +2714*a(n-4) +14822*a(n-5) +40045*a(n-6) -13074*a(n-7) -188866*a(n-8) -146746*a(n-9) -2847627*a(n-10) -28326996*a(n-11) -83583759*a(n-12) -58134679*a(n-13) -55071639*a(n-14) -935476281*a(n-15) -2941843570*a(n-16) -4647953916*a(n-17) -6802814009*a(n-18) -10276372690*a(n-19) +4606444204*a(n-20) -10790406963*a(n-21) -223098127900*a(n-22) -376509702724*a(n-23) -284916996543*a(n-24) -510849498127*a(n-25) +860067107185*a(n-26) +1908174610309*a(n-27) +1719064965533*a(n-28) +4757780178617*a(n-29) -2559161517916*a(n-30) +1117601478747*a(n-31) -1011378713829*a(n-32) -12424503170829*a(n-33) +18323418282582*a(n-34) -43747124015672*a(n-35) +53298075764133*a(n-36) -3343299962709*a(n-37) +73788259658971*a(n-38) +78108426967720*a(n-39) -54681946411006*a(n-40) -704782356131*a(n-41) -184705962402654*a(n-42) -84382794252318*a(n-43) +65484731585469*a(n-44) +20412472234727*a(n-45) +300102089956786*a(n-46) -31181093572314*a(n-47) +99010720999383*a(n-48) -196569534925309*a(n-49) -76120095466160*a(n-50) -70012269381224*a(n-51) -66395600958028*a(n-52) +180534054366095*a(n-53) +22404716004294*a(n-54) +88114487446760*a(n-55) -62235301656822*a(n-56) -96245646946438*a(n-57) +26980781909964*a(n-58) -36539671934151*a(n-59) +20150617586286*a(n-60) +18267859633053*a(n-61) -4866073561101*a(n-62) -10871073571114*a(n-63) -8212218057172*a(n-64) +11934276481294*a(n-65) -2431374694673*a(n-66) -4791807166894*a(n-67) +2652173409510*a(n-68) +362500705896*a(n-69) -291523398408*a(n-70) -93534736781*a(n-71) +50745103150*a(n-72) -76138859216*a(n-73) +45265643821*a(n-74) -5449168807*a(n-75) -487513235*a(n-76) -469952803*a(n-77) +589870484*a(n-78) -514000179*a(n-79) +225488643*a(n-80) -57373941*a(n-81) +9486365*a(n-82) -100413*a(n-83) -228735*a(n-84) +28012*a(n-85) -7833*a(n-86) +3962*a(n-87) -1348*a(n-88) -33*a(n-89) +18*a(n-90) for n>92

Example

Some solutions for n=5
..0..0..1..1....0..0..1..1....0..2..1..1....0..0..0..2....0..2..1..0
..1..0..0..0....1..2..0..0....2..0..0..2....0..2..2..0....0..0..1..0
..1..0..1..1....1..2..0..0....1..1..0..0....0..1..1..0....0..0..0..0
..2..0..0..0....0..0..2..2....0..0..0..0....1..0..0..0....0..0..2..2
..0..0..1..1....2..0..2..0....2..0..1..1....1..0..1..1....2..0..2..0

Crossrefs

Sequence in context: A214132 A196703 A196852 * A090407 A222915 A367531

Adjacent sequences: A196943 A196944 A196945 * A196947 A196948 A196949

Keyword

nonn

Author

R. H. Hardin Oct 08 2011

Status

approved